System for recognizing multiple object input and method and product for same

ABSTRACT

Methods, systems, and computer program products are provided for the recognition of input of multiple objects into a computing device, wherein the computing device has a processor and at least one application for recognizing the input under control of the processor. The application is configured to determine at least one geometrical feature of a plurality of elements of the input, and compare the determined at least one geometrical feature with at least one pre-determined geometrical threshold to determine a positive or negative result. If the comparison yields a negative result, the application considers the elements as belonging to one object in the recognition of the input. If the comparison yields a positive result, the application considers the elements as belonging to multiple objects in the recognition of the input.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to European Application No. 15290183.1filed on Jul. 10, 2015, the entire contents of which is incorporated byreference herein.

TECHNICAL FIELD

The present invention relates generally to the field of computing deviceinterfaces capable of recognizing input of multiple handwritten objects.

BACKGROUND

The ubiquity of computing devices to daily life continues to grow. Theytake the form of personal and professional desktops, laptops, hybridlaptops, tablet PCs, e-book readers, mobile phones, smartphones,wearable computers, global positioning system (GPS) units, enterprisedigital assistants (EDAs), personal digital assistants (PDAs), gameconsoles, and the like.

Computing devices generally consist of at least one processing element,such as a central processing unit (CPU), some form of memory, and inputand output devices. The variety of computing devices and theirsubsequent uses necessitate a variety of input devices. One such inputdevice is a touch sensitive surface such as a touch screen or touch padwherein user input is received through contact between the user's fingeror an instrument such as a pen or stylus and the touch sensitivesurface. Another input device is an input surface that senses gesturesmade by a user above the input surface. Either of these methods of inputcan be used generally for drawing or inputting so-called digital ink toexpress text, symbols, etc., which the computing device interprets usinghandwriting recognition systems or methods. Other systems forhandwriting input to computing devices include electronic or digitalpens which interact with paper, encoded surfaces or digitizing surfacesin order to have their movement relative to the surface tracked by acomputing device, such as the systems provided by Anoto AB., LeapfrogEnterprises, Inc., and Livescribe, Inc.

Regardless of the input method used, handwriting recognition systems andmethods typically involve determining the initiation of a digital inkstroke, such as when first contact with a touch sensitive surface ismade (pen-down event); the termination of the stroke, such as whencontact with the touch sensitive surface is ceased (pen-up event); andany movement (gestures or strokes) made between stroke initiation andtermination. These determined strokes are processed to interpret theinput which is usually performed in several stages includingpreprocessing, segmentation, recognition, and interpretation. Generally,the preprocessing stage involves discarding irrelevant input data andnormalizing, sampling, and removing noise from relevant data. Thesegmentation stage specifies the different ways to break down the inputdata into individual elements to be recognized depending on the type ofinput, e.g., characters, words, symbols, objects, or shapes. Therecognition stage generally includes a feature extraction stage, whichcharacterizes the different input segments, and a classification stagewhich associates the segments with possible recognition candidates. Theinterpretation stage generally involves identifying the elementsassociated with the candidates. Less, more, or different stages are alsopossible.

The type of computing device or input surface can also determine thetype of handwriting recognition system or method utilized. For instance,if the input surface is large enough (such as a tablet), the user canhandwrite input anywhere on or above the input surface, as if the userwas writing on paper. This however adds complexity to the recognitiontask, because the separate elements to be recognized may be relateddependent of the relative positions of the elements or may be unrelatedindependent of their relative positions.

For example, one desired use for handwriting recognition is innote-taking for the capture of mathematical equations or expressions,physics concepts, chemistry formulas, musical notation, etc., duringeducation sessions, such as classes or lectures. That is, a student maywish to write multiple equations over several lines to express theworking of a mathematical problem which the educator has demonstrated(which could also be in digital ink) or which the student is required tosolve as an assignment or assessment, or the educator may wish toprepare a worksheet for students involving a list of non-relatedequations that define a set of problems to be solved by the student,either manually or automatically by the computing device, or the captureof a system of equations or vector/matrix may be desired. The need forthe entry of multiple connected or un-connected expressions may alsooccur in enterprise settings, such as during budget setting meetings,technology research and development sessions, technical documentation,etc., or in personal settings, such as a consumer writing a longaddition over several lines whilst grocery shopping in order tocalculate the total amount.

Systems for the recognition of handwritten mathematical equations areknown. These systems concentrate on determining the elements of inputequations through matching against databases/lexicons containing knownmathematical symbols and relationships. These systems generallyrecognize the elements without any consideration of the actual contentor structure of the equations themselves. As such when multipleequations are entered, say in a vertical list, it is possible that therecognition may consider elements of intended separate equations tobelong to the same equation, or at least the recognition element willform and test hypotheses with respect to this. This of coursesubstantially increases recognition processing and time, and decreasesrecognition accuracy.

Some known systems relate to providing calculations or likely solutionsof input equations, and therefore may take the content into account.However, these systems do not recognize multiple equations input either,rather they recognize the input of mathematical operators, such as theequals sign or a result line, or user gestures, to determine when asolution is to be provided to the currently input equation, such thatthe next input is inherently another separate equation or an edit to thecurrent equation, see for example European Patent No. 0 676 065.

Other known systems provide recognition of systems of equations andtabular structures, such as matrices, involving equations. However,these systems rely on indicative elements for recognition, such asbrackets or spatial alignment, e.g., within rows and columns, and assuch do not recognize multiple equations as such rather a structureinvolving multiple inputs of any type, see for example U.S. Pat. No.7,447,360.

What is required is a system that recognizes multiple equation inputsindependent of links between the equations that do not rely on the inputof specific designation elements or gestures and do not significantlyincrease processing time or complexity to the recognition of theequations themselves whilst retaining sufficient recognition accuracy.

SUMMARY

The examples of the present method, system, and computer program productare described herein below as providing the recognition of input ofmultiple objects into a computing device, wherein the computing devicehas a processor and at least one method or system for recognizing theinput under control of the processor.

In an aspect of the disclosed method, system, and computer programproduct the disclosed system and method determines at least onegeometrical feature of a plurality of elements of the input, andcompares the at least one geometrical feature with at least onepre-determined geometrical threshold to determine a positive or negativeresult. If the comparison yields a negative result, the disclosed methodor system considers the elements as belonging to one object in therecognition of the input. If the comparison yields a positive result,the method or system considers the elements as belonging to multipleobjects in the recognition of the input.

The at least one geometrical feature may include one or more distancesbetween pairs of elements of the plurality of elements. The one or moredistances may be between one or more factors of the content of eachelement of each pair of elements. The one or more factors may include atleast one of a factor common to the elements of each pair of elementsand a geometrical boundary including each element.

Each element of each pair of elements may represent one or morehandwritten strokes, such that the common factor is the barycenter ofthe one or more strokes, the at least one pre-determined geometricalthreshold is a barycenter distance threshold, and the comparison yieldsa positive result if the barycenter distance determined for a pair ofelements is greater than the barycenter distance threshold, such thatthe elements of the pair of elements are considered as belonging todifferent objects.

The at least one pre-determined geometrical threshold may be ageometrical boundary distance threshold, such that the comparison yieldsa positive result if the geometrical boundary distance determined for apair of elements is greater than the geometrical boundary distancethreshold, such that the elements of the pair of elements are consideredas belonging to different objects.

The comparison may include comparing a first distance with a firstpre-determined distance threshold and a second distance with a secondpre-determined distance threshold for each pair of elements. In thiscase, the comparison yields a positive result for a pair of elements ifboth the first and second distances are greater than the respectivefirst and second pre-determined distance thresholds, such that theelements of the pair of elements are considered as belonging todifferent objects. For each pair of elements, the first distance may thedistance between the common factor of the elements and the seconddistance may be the distance between the geometrical boundary of theelements, such that the first pre-determined distance threshold is acommon factor distance threshold, and the first pre-determined distancethreshold is a geometrical boundary threshold.

The elements of each pair of elements may be geometrically adjacent, andthe method or system may be configured to determine at least one of apositional and temporal order of input of the elements of the pluralityof elements.

The at least one geometrical threshold may be pre-determined withconsideration of the determined temporal order of input of the elements.

For at least one pair of the pairs of elements, the method or system maybe configured to determine the at least one geometrical feature bydetermining the geometrical boundary distances between pairs of elementswhich each contain a first element having a first positional orderrelationship with one element of the at least one pair and a secondelement having a second positional order relationship with the otherelement of the at least one pair, and determining the minimum distanceof the determined geometrical boundary distances. In this case, the atleast one pre-determined geometrical threshold includes a geometricalboundary distance threshold, such that the comparison includes comparingthe determined minimum geometrical boundary distance with thegeometrical boundary distance threshold, and the comparison yields apositive result if the determined minimum geometrical boundary distanceis greater than the geometrical boundary distance threshold, such thatthe elements of the at least one pair are considered as belonging todifferent objects.

The positional order may be directional, with the first and seconddirectional relationships being first and second directions from theelements of the at least one pair, respectively.

The pairs of first and second elements may contain first elements withina geometrical area of the second element. In this case, each element ofeach pair of elements represents one or more handwritten strokes, andthe geometrical area is based on a characteristic of the one or morehandwritten strokes.

The multiple objects may be one or more geometrical separatedhandwritten mathematical equations, with the elements being handwrittencharacters, symbols and operators of each of the multiple mathematicalequations.

BRIEF DESCRIPTION OF THE DRAWINGS

The present system and method will be more fully understood from thefollowing detailed description of the examples thereof, taken togetherwith the drawings. In the drawings like reference numerals depict likeelements. In the drawings:

FIG. 1 shows a block diagram of a computing device in accordance with anexample of the present system and method;

FIG. 2 shows a block diagram of a system for handwriting recognition inaccordance with an example of the present system and method;

FIG. 3 shows a block diagram illustrating detail of the handwritingrecognition system of FIG. 2 in accordance with an example of thepresent system and method;

FIG. 4 shows an example of handwritten mathematical equations input inaccordance with the present system;

FIG. 5 shows an example of handwritten mathematical equations input inaccordance with the present system;

FIG. 6 shows an example multiple object input in accordance with thepresent system and method;

FIG. 7 shows a flow diagram of an example of the present system andmethod for recognizing a multiple object input to the computing device;

FIG. 8 shows an example of a handwritten mathematical equation input inaccordance with the present system;

FIG. 9 shows the example multiple object input of FIG. 6 with time-orderdetail;

FIGS. 10A-10C show an example of the present system for recognizing amultiple object input in accordance with the present system and method;

FIGS. 11A-11D show an example of the present system for recognizing amultiple object input in accordance with the present system and method;

FIGS. 12A and 12B show an alternative example of the method or system ofFIG. 11 in accordance with the present system and method;

FIG. 13 shows a flow diagram of the example methods of FIGS. 10-12;

FIG. 14 shows a flow diagram of a portion of the flow diagram of FIG.13;

FIG. 15 shows a flow diagram of another portion of the flow diagram ofFIG. 13;

FIG. 16 shows another example of a handwritten mathematical equationinput in accordance with the present system; and

FIG. 17 shows a flow diagram of an alternative portion of the flowdiagram of FIG. 13 as applied to the examples of FIG. 12.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth by way of examples in order to provide a thorough understanding ofthe relevant teachings. However, it should be apparent to those ofordinary skill in the art that the present teachings may be practicedwithout such details. In other instances, well known methods,procedures, components, and/or circuitry have been described at arelatively high-level, without detail, in order to avoid unnecessarilyobscuring aspects of the present teachings. Reference to and discussionof directional features such as up, down, above, below, lowest, highest,horizontal, vertical, etc., are made with respect to the Cartesiancoordinate system as applied to the input surface on which the input tobe recognized is made.

The various technologies described herein generally relate to multiplehandwritten object recognition. The system and method described hereinmay be used to recognize a user's natural writing or drawing style inputto a computing device through the processes of pre-processing andrecognition. The user's input to the computing device can be made via aninput surface, such as a touch sensitive screen, connected to, or of,the computing device or via an input device, such as a digital pen ormouse, connected to the computing device. Whilst the various examplesare described with respect to recognition of handwriting input usingso-called online recognition techniques, it is understood thatapplication is possible to other forms of input for recognition, such asoffline recognition (ICR) in which images rather than digital ink arerecognized.

FIG. 1 shows a block diagram of an example computing device 100. Thecomputing device may be a computer desktop, laptop, tablet PC, e-bookreader, mobile phone, smartphone, wearable computer, digital watch,interactive whiteboard, global positioning system (GPS) unit, enterprisedigital assistant (EDA), personal digital assistant (PDA), game console,or the like. Computing device 100 includes at least one processingelement, some form of memory and input and/or output (I/O) devices. Thecomponents communicate with each other through inputs and outputs, suchas connectors, lines, buses, cables, buffers, electromagnetic links,networks, modems, transducers, IR ports, antennas, or others known tothose of ordinary skill in the art.

The computing device 100 has at least one display 102 for outputtingdata from the computing device such as images, text, and video. Thedisplay 102 may use LCD, plasma, LED, iOLED, CRT, or any otherappropriate technology that is or is not touch sensitive as known tothose of ordinary skill in the art. At least some of display 102 isco-located with at least one input surface 104. The input surface 104may employ technology such as resistive, surface acoustic wave,capacitive, infrared grid, infrared acrylic projection, optical imaging,dispersive signal technology, acoustic pulse recognition, or any otherappropriate technology as known to those of ordinary skill in the art toreceive user input. The input surface 104 may be bounded by a permanentor video-generated border that clearly identifies its boundaries.

In addition to the input surface 104, the computing device 100 mayinclude one or more additional I/O devices (or peripherals) that arecommunicatively coupled via a local interface. The additional I/Odevices may include input devices such as a keyboard, mouse, scanner,microphone, touchpads, bar code readers, laser readers, radio-frequencydevice readers, or any other appropriate technology known to those ofordinary skill in the art. Further, the I/O devices may include outputdevices such as a printer, bar code printers, or any other appropriatetechnology known to those of ordinary skill in the art. Furthermore, theI/O devices may include communications devices that communicate bothinputs and outputs such as a modulator/demodulator (modem; for accessinganother device, system, or network), a radio frequency (RF) or othertransceiver, a telephonic interface, a bridge, a router, or any otherappropriate technology known to those of ordinary skill in the art. Thelocal interface may have additional elements to enable communications,such as controllers, buffers (caches), drivers, repeaters, andreceivers, which are omitted for simplicity but known to those of skillin the art. Further, the local interface may include address, control,and/or data connections to enable appropriate communications among theother computer components.

The computing device 100 also includes a processor 106, which is ahardware device for executing software, particularly software stored inthe memory 108. The processor can be any custom made or commerciallyavailable general purpose processor, a central processing unit (CPU), asemiconductor based microprocessor (in the form of a microchip orchipset), a macroprocessor, microcontroller, digital signal processor(DSP), application specific integrated circuit (ASIC), fieldprogrammable gate array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, statemachine, or any combination thereof designed for executing softwareinstructions known to those of ordinary skill in the art. Examples ofsuitable commercially available microprocessors are as follows: aPA-RISC series microprocessor from Hewlett-Packard Company, an 80×86 orPentium series microprocessor from Intel Corporation, a PowerPCmicroprocessor from IBM, a Sparc microprocessor from Sun Microsystems,Inc., a 68xxx series microprocessor from Motorola Corporation, DSPmicroprocessors, or ARM microprocessors.

The memory 108 can include any one or a combination of volatile memoryelements (e.g., random access memory (RAM, such as DRAM, SRAM, orSDRAM)) and nonvolatile memory elements (e.g., ROM, EPROM, flash PROM,EEPROM, hard drive, magnetic or optical tape, memory registers, CD-ROM,WORM, DVD, redundant array of inexpensive disks (RAID), another directaccess storage device (DASD)). Moreover, the memory 108 may incorporateelectronic, magnetic, optical, and/or other types of storage media. Thememory 108 can have a distributed architecture where various componentsare situated remote from one another but can also be accessed by theprocessor 106. Further, the memory 108 may be remote from the device,such as at a server or cloud-based system, which is remotely accessibleby the computing device 100. The memory 108 is coupled to the processor106, so the processor 106 can read information from and writeinformation to the memory 108. In the alternative, the memory 108 may beintegral to the processor 106. In another example, the processor 106 andthe memory 108 may both reside in a single ASIC or other integratedcircuit.

The software in memory 108 includes an operating system 110,applications 112 and a handwriting recognition (HWR) system 114, whichmay each include one or more separate computer programs, each of whichhas an ordered listing of executable instructions for implementinglogical functions. The operating system 110 controls the execution ofthe applications 112 and the HWR system 114. The operating system 110may be any proprietary operating system or a commercially availableoperating system, such as WEBOS, WINDOWS®, MAC and IPHONE OS®, LINUX,and ANDROID. It is understood that other operating systems may also beutilized.

The applications 112 may be related to handwriting recognition asdescribed herein, different functions, or both. The applications 112include programs provided with the computing device 100 upon manufactureand may further include programs uploaded or downloaded into thecomputing device 100 after manufacture. Some examples include a texteditor, telephone dialer, contacts directory, instant messagingfacility, computer-aided design (CAD) program, email program, wordprocessing program, web browser, and camera.

The HWR system 114, with support and compliance capabilities, may be asource program, executable program (object code), script, application,or any other entity having a set of instructions to be performed. When asource program, the program needs to be translated via a compiler,assembler, interpreter, or the like, which may or may not be includedwithin the memory, so as to operate properly in connection with theoperating system. Furthermore, the handwriting recognition system withsupport and compliance capabilities can be written as (a) an objectoriented programming language, which has classes of data and methods;(b) a procedure programming language, which has routines, subroutines,and/or functions, for example but not limited to C, C++, Pascal, Basic,Fortran, Cobol, Perl, Java, Objective C, Swift, and Ada; or (c)functional programming languages for example but no limited to Hope,Rex, Common Lisp, Scheme, Clojure, Racket, Erlang, OCaml, Haskell,Prolog, and F#. Alternatively, the HWR system 114 may be a method orsystem for communication with a handwriting recognition system remotefrom the device, such as server or cloud-based system, but is remotelyaccessible by the computing device 100 through communications linksusing the afore-mentioned communications I/O devices of the computingdevice 100.

Strokes entered on or via the input surface 104 are processed by theprocessor 106 as digital ink. A user may enter a stroke with a finger orsome instrument such as a pen or stylus suitable for use with the inputsurface. The user may also enter a stroke by making a gesture above theinput surface 104 if technology that senses motions in the vicinity ofthe input surface 104 is being used, or with a peripheral device of thecomputing device 100, such as a mouse or joystick. A stroke ischaracterized by at least the stroke initiation location, the stroketermination location, and the path connecting the stroke initiation andtermination locations. Because different users may naturally write thesame object, e.g., a letter, a shape, or a symbol, with slightvariations, the present system accommodates a variety of ways in whicheach object may be entered whilst being recognized as the correct orintended object.

FIG. 2 is a schematic pictorial of an example of the HWR system 114. TheHWR system 114 includes stages such as preprocessing 116, recognition118 and output 120. The preprocessing stage 116 processes the digitalink to achieve greater accuracy and reducing processing time during therecognition stage 118. This preprocessing may include normalizing of thepath connecting the stroke initiation and termination locations byapplying size normalization and/or methods such as B-splineapproximation to smooth the input. The preprocessed strokes are thenpassed to the recognition stage 118 which processes the strokes torecognize the objects formed thereby. The recognized objects are thenoutput 120 to the display 102 generally as a typesetted version of thehandwritten elements/characters.

The recognition stage 118 may include different processing elements orexperts. FIG. 3 is a schematic pictorial of the example of FIG. 2showing schematic detail of the recognition stage 118. Three experts(segmentation expert 122, recognition expert 124, and language expert126) are illustrated which collaborate through dynamic programming togenerate the output 120.

The segmentation expert 122 defines the different ways to segment theinput strokes into individual element hypotheses, e.g., alphanumericcharacters and mathematical operators, text characters, individualshapes, or sub expression, in order to form expressions, e.g.,mathematical equations, words, or groups of shapes. For example, thesegmentation expert 122 may form the element hypotheses by groupingconsecutive strokes of the original input to obtain a segmentation graphwhere each node corresponds to at least one element hypothesis and whereadjacency constraints between elements are handled by the nodeconnections.

The recognition expert 124 provides classification of the featuresextracted by a classifier 128 and outputs a list of element candidateswith probabilities or recognition scores for each node of thesegmentation graph. Many types of classifiers exist that could be usedto address this recognition task, e.g., Support Vector Machines, HiddenMarkov Models, or Neural Networks such as Multilayer Perceptrons, Deep,Convolutional or Recurrent Neural Networks. The choice depends on thecomplexity, accuracy, and speed desired for the task.

The language expert 126 generates linguistic meaning for the differentpaths in the segmentation graph using language models (e.g., grammar orsemantics). The expert 126 checks the candidates suggested by the otherexperts according to linguistic information 130. The linguisticinformation 130 can include a lexicon, regular expressions, etc. Thelanguage expert 126 aims at finding the best recognition path. In oneexample, the language expert 126 does this by exploring a language modelsuch as final state automaton (determinist FSA) representing the contentof linguistic information 130. In addition to the lexicon constraint,the language expert 126 may use statistical information modeling for howfrequent a given sequence of elements appears in the specified languageor is used by a specific user to evaluate the linguistic likelihood ofthe interpretation of a given path of the segmentation graph.

The system and method described herein makes use of the HWR system 114in order to recognize multiple equations. Multiple equations are definedas the layout of several equations on one or more pages. The equationscan be linked (e.g., a sequence or system of equations, showingdifferent steps of a demonstration) or not (e.g., several exercises on atopic).

FIG. 4 illustrates an example of a vertical list 400 of handwrittenmathematical equations or expressions 401-404, which has been input viathe input surface 104. Each equation has been written on separate lines405-408 (these lines may be actually displayed on the display 102 toguide user input, but this is not necessary). Each equation isindependent of the other equations, being complete un-linked operations.Further, each equation is relatively simple, being division ormultiplication operations of two numbers with a single number result.

If only the first handwritten equation 401 was present, say, therecognition stage 118 would create and test multiple hypotheses usingits experts. The candidates for each element within the equation 401,i.e., ‘3’, ‘5’, ‘÷’, ‘7’, ‘=’ and ‘5’ would be considered and scored toprovide the output 120 of the recognized typesetted versions of theelements, i.e., ‘35÷7=5’. In order to create the hypotheses, manycandidates are considered including various concatenations of theindividual segmented strokes of each element.

However, since the subsequent handwritten equations 402-404 are presentin the example of FIG. 4 without explicit recognition of there beingmultiple equations or detection of certain mathematical operates, therecognition stage 118 would be required to create and test multiplehypotheses using its experts for not only the elements within the firstequation 401 but also for the elements in all four equations, whichincreases the level of processing and influences the possiblerecognition accuracy. This extra processing would be necessary becausemathematical or arithmetical equations are two-dimensional (2D), e.g.,horizontal and vertical. This is different than text, where each line oftext is substantially one-dimensional (1D), e.g., horizontal (with theexception of superscript and subscript text which can be dealt with bythe language expert, for example), such that only inter-line hypothesesare created and tested during text recognition is the presence of wordsthat are split over the lines (e.g., with hyphenation). Therefore, itcannot be assumed that multiple equations are present just becausemultiple lines are present. For example, the equation 401 could bewritten with ‘35’ as the nominator, ‘7’ as the denominator, and the ‘÷’symbol as a dividing line. The equation 401 would then occupy more thanone vertical line in that form.

FIG. 5 illustrates a vertical list 500 of multiple handwritten equationsin which re-expression of an initial equation 501 over multipleequations 502-504 is input. As can be seen, each of the equations501-504 includes both horizontally displaced and vertically displacedelements.

This also applies to any handwritten input of a 2D system of objects,such as drawings, geometrical sketches, charts, graphs, diagrams,tables, circuits, music, chemical formulas, etc., in which multipleobjects are input and need to be separately recognized. Detecting thepresence of multiple 2D objects prior to creating extraneous hypothesestherefore assists in the reducing recognition processing overhead (e.g.,time and memory resources) and in the increasing recognition accuracy(e.g., unintended but otherwise probable candidates based on the expertmodels are not tested).

One method of detecting multiple input objects would be to requirespecific user action, such as creating a new writing area, tapping a newobject/line physical or virtual button, inputting certain handwrittengestures—e.g., a downward stroke—or other interactions—e.g., a tap onthe input surface in order to indicate the end of input of an object.However, such specific user actions would not provide a satisfactoryexperience for the users as they are not included in naturalhandwriting. The recognition process of multiple 2D objects should notbe affected in a way that reduces the users' experience of the system orwhich places constraints on the type of input that will be recognized.For example, the recognition of mathematical operator symbols in theequations, such as the equals symbol ‘=’ in FIGS. 4 and 5, could be usedto detect the input of multiple equations. However, this assumptionwould restrict users from using multiple equalities on one line—e.g.,(x+1)(x+2)=x²+2x+x+2=x²+3x+2—or starting equations with operators—e.g.,writing ‘=’ as the first element in the development of a demonstrationor working of a problem or writing ‘+’ as the first element as acontinuation of the equation written on the previous line.

Another example of the recognition stage 118 for detection of multiple2D objects input as a vertical list includes the determination of emptyvertical space (i.e., space of the input surface 104 on whichhandwritten strokes are not input) between vertically displacedhandwritten objects using geometrical features of elements of the inputobjects. Vertical empty space greater than a predetermined size, e.g., athreshold, is detected. This is a process of ‘cutting’ the input intosections to classify or filter those cuts above the threshold as being aspace between individual objects, such as equations. All elements overmultiple lines are not considered in subsequent processing by theexperts of the recognition stage 118 as belonging to the same equation.This significantly cuts down the number of hypotheses created andtested. The classification is performed by allocating one or moregeometrical costs. The threshold includes (vertical) geometricalcost(s), which is adjustable so that the filtering can be performed inorder to optimize or train the filtering process to determine suitablethreshold levels that optimize multiple object detection withoutreturning a substantial number of false positives. This example issimilarly applicable in the horizontal direction.

FIG. 6 illustrates an example of a vertically displaced multiple objectinput 600 on the input surface 104, and FIG. 7 is a flow diagram of anexample method 700 for recognizing the multiple object input 600. Themultiple object input 600 includes multiple elements 601-609 illustratedas boxes containing one or more handwritten strokes that have beeninput. The boxes may be bounding boxes around the extent of each strokeor set of strokes of an element. Each of the elements 601-609 has beenwritten with horizontal (designated as the ‘x’ direction) and/orvertical (designated as the ‘y’ direction) displacement with respect toeach of the other elements 601-609. However, the elements 601-604 aregenerally written in a first horizontal group 610 (i.e., along dashedhorizontal line a) and elements 605-609 are generally written in asecond horizontal group 611 (i.e., along dashed horizontal line a′),where line a is vertically displaced from line a′. The first group ofelements may represent a first equation and the second group of elementsmay represent a second equation.

The input of handwritten strokes are received (step 701) and theelements are determined (step 702). It is then determined if groups ofthe elements can be established (step 703). If they cannot, the elementsare sent to the next stage to create hypotheses using all input strokes(step 704). If the elements can be grouped, a bounding box isestablished about each group (step 705). In FIG. 6, a first bounding box612 is established about the first group 610 of elements and a secondbounding box 613 is established about the second group 611 of elements.These groupings and bounding boxes are reassessed and adjusted if morestrokes are received (step 706).

Then it is determined if adjacent groups are present (step 707). If so,‘cut’ lines at adjacent bounding box edges are established in the yand/or x directions depending on the application (step 708). In FIG. 6,a potential first horizontal cut line b is established at the lowest(i.e., in the y direction) edge of bounding box 612 and a potentialsecond horizontal cut line b′ is established at the highest (i.e., inthe y direction) edge of bounding box 613. The geometrical feature ofthe distance between adjacent cut lines is calculated/measured todetermine a geometrical cost for use in the next recognition stage, canbe done by a pixel count (step 709). The calculated distance is thencompared to a pre-determined threshold distance (step 710), where thepre-determination of the threshold may be made in consideration of thepixel resolution of the input surface 104. In FIG. 6, for example, thedistance c between cut lines b and b′ represents the height of the emptyspace between the two element groups being the closest vertical distancebetween the two groups, which is the distance between the lowest elementof the first group 610, being the element 603, and the highest elementof the second group 611, being the element 607.

If the geometrical cost is above the threshold, the first and secondgroups represent two separate 2D objects, such as two equations, and thenext recognition stage hypotheses does not involve elements of adjacentmultiple objects being created or tested (step 711). This simplifiesrecognition and increases recognition speed. On the other hand, if thegeometrical cost is below the threshold, hypotheses for all elements ofthe determined groups have to be created and tested by the nextrecognition stage (step 712).

The example shown in FIG. 7 is an iterative process that may beperformed as handwritten strokes are input. Alternatively, the processmay be performed on previously input information, such that step 706 isomitted and steps 701-705 are performed for all strokes before launchinginto the geometrical cost test of steps 707-712. Therefore, thedetermination of multiple element input and grouping of the elements,through determination of the positional order of the elements, isperformed prior to the multiple object recognition process.

The setting of the threshold described in FIGS. 6 and 7 is done so ahigh level of confidence is achieved if geometrical cost alone is to beused to determine separate vertically displaced objects. However, it isunderstood the geometrical cost threshold is adjustable depending on theapplication or type of handwritten input and level of confidencerequired. For example, handwritten input of mathematical symbols, withina single equation the size and relative positioning of eachstroke/element can vary greatly. Vertical overlapping of severalelements can occur, and vertical displacement over several lines canalso occur, as in FIG. 8. In such a case, the confidence level must behigher in order to accept vertical geometrical cost alone as anindicator of multiple equation input. Adjustment of geometrical costthreshold may be provided through a lookup table or like system in whichcertain thresholds are predefined based on application and otherfactors, such as stroke size, number of stokes, etc.

In the example described above, vertically separated input is searchedby establishing groups of horizontally displaced elements. These groupsmay first be established by performing a search for horizontal emptyspace between horizontally adjacent elements until there are no morehorizontally adjacent elements. Those elements are considered a group,and a bounding box is established about the boundary thereof to containall elements in both the x and y directions. This grouping may berefined by setting a horizontal distance threshold or horizontalgeometrical cost, so elements or groups of elements that arehorizontally displaced by a large distance are not grouped together. Forexample, mathematical equations may not be expected to have large gapsin a single equation, whereas in drawing input large gaps betweendrawing elements may be intended for geometrical information.

Grouping may also be made based on positional relationships other than avertical relationship, including horizontal relationships forhorizontally displaced elements which overlap vertically—e.g., elements601-604—or general positional relativity such as geometrical features.This grouping may be based on elements sharing a common trend-line orvirtual center of gravity in the y-direction. This could be based on thecommon geometrical features of the strokes themselves (e.g., thebarycenter) or common or non-common geometrical features of the elements(e.g., edges of the bounding boxes, mean center-lines of the y-directionextents of each bounding box, the horizontal lines a and a′ in FIG. 6,or different edges of the elements themselves). Further, the verticaldistance d between the common lines a and a′ could be used instead of,or additional to, the vertical distance c to establish the geometricalcost or a plurality of geometrical costs.

The above steps of the recognition stage 118 can be considered as‘pre-processing’ or ‘filtering’ based on a threshold with the purpose ofreducing the number of possibilities (and so the processing time) to cutthe handwritten input into individual objects. Accordingly, this processmay be carried out in either preprocessing 116 or the recognition stage118, depending on the computer device 100. The confidence applied tothis filtering depends on the application and type of handwritten input,as well as the desired level of accuracy. Further, this filtering mayalso be part of the decision making process for recognizing multipleobjects, such as a vertical list of equations. The recognition stage 118may be supplemented with consideration of other factors to create andexplore different segmentation hypotheses, for example, using thegrammar and language models. Accordingly, the threshold may factor inmore than the geometrical cost for optimization.

For instance, the threshold may factor in the temporal or time-orderentry of the strokes/elements. By taking the time-order of input intoaccount, success of filtering is enhanced for instance in the horizontalinput of a group of elements followed by a second group of one or moreelements vertically displaced from the first group indicates potentialmultiple object entry, such as multiple equations. Whereas, the verticalinput of a group of elements followed by the input of one or moreelements horizontally displaced from the first group may indicate, asingle equation having vertical functions, e.g., divisions.

FIG. 9 illustrates input 600 of FIG. 6 using the time-order. Theelements 601-609 are input in the time-order t₁-t₉, respectively. Thedetermination of input timing is known to those of skill in the art, andmay include the monitoring and storing of the time stamp of thecompletion of a stroke, e.g., at pen-up, as determined from the systemclock of the operating system 110. From this time-order, a time cost canbe supplemented with the geometrical cost for the next step of therecognition stage 118.

For example, element 604 is vertically displaced from element 605, andelement 604 is horizontally displaced by a relatively large horizontaldistance from element 605. A similar horizontal distance exists betweenelements 601 and 604, but there are intervening elements 602 and 603.All of this relative geometrical information could be used to determinewhether the element 605 belongs to a new object or at least does notbelong to the element group 610. However, the geometrical cost may bebelow, but near, the geometrical cost threshold such that the system isnot confident of multiple equation detection. If the system usestime-order information to determine element 604 was input at time t₄directly before the input of the element 605 at time t₅ the time-orderdifference, being the time cost, could be used to boost the geometricalcost to be above the geometrical cost threshold. A combined thresholdcould be set in which the geometrical and time costs are compared. Aweighted threshold could also be used to apply different weightings tothe geometrical cost threshold based on the time-order.

Other factors can also be used to hone the multiple object detectionthrough the setting of combined thresholds and/or adjustment ofcalculated costs for comparison with the threshold(s). These factorsinclude absolute and relative locations of the elements (e.g.,determination of barycenter or relative distances between adjacentelements), which may be most useful when the time-order is not alignedwith the position-order (e.g., if in FIG. 9, element 604 was input priorto elements 602 and 603, which often occurs in handwritten equationinput due to the types of operations and formulas being captured).Further, the language model(s) of the language expert may be used todetermine if the input of certain elements and their relative placementwith respect to other elements indicates single or multiple objects, forexample, a mathematical or arithmetical language model may interpret along horizontal element (e.g., a single stroke) vertically displacedfrom one or more adjacent elements as indicating a division rather thanmultiple equations. Furthermore, the number of strokes in individual andadjacent/grouped elements may also be taken into account, either aloneor in consideration of the language model(s). For example, a relativelysmall number of strokes may indicate input of a single object whereas arelatively large number of strokes may indicate multiple objects.

The above described recognition of a vertical list of objects based ongrouping of horizontally displaced elements has the purpose of reducingthe processing through not considering the geometrical relationshipbetween all vertically separated objects when creating hypotheses forrecognition in subsequent recognition processing. While processing speedis important to the user experience, accuracy of the recognition is justas important. Typically handwriting recognition systems compromisebetween speed and accuracy, increasing accuracy typically increasesprocessing time and decreasing processing time typically decreasesaccuracy. In order to provide an effective system, a balance betweenthese factors needs to be found. In the alternative, the followingexample includes multiple geometrical costs to provide a better balancebetween time and accuracy.

FIGS. 10A-10C show steps in an example recognition stage 118 for avertically displaced multiple object input 1000. FIGS. 11A-11D showsteps in the example recognition stage as applied to another element ofthe input 1000. FIGS. 12A and 12B show steps in an alternative examplerecognition system and method as applied to the elements of FIG. 11.

The input 1000 includes multiple elements 1001-1006 illustrated as boxescontaining one or more handwritten input strokes. The boxes may bebounding boxes around the extent of each stroke or set of strokes of anelement. Each of the elements 1001-1006 has been written with horizontal(designated as the ‘x’ direction) and/or vertical (designated as the ‘y’direction) displacement with respect to each of the other elements1001-1006. In order to recognize whether elements 1001-1006 belong toone or more vertically displaced objects, process 1300 is performed asillustrated in the flow diagram of FIG. 13.

This process begins with the determination of the number n of elementspresent (i.e., n=6 in the present example) representing the input ofmultiple handwritten strokes (step 1301). The y-order, being apositional or directional order of entry in the y-direction, of these nelements is then determined (step 1302) as Y₁ to Y_(n). In the presentexample as depicted in FIG. 10A, the elements 1001-1006 are respectivelydetermined to have the y-order Y₁-Y₆. Element 1001 has y-order Y₁, andelement 1006 has y-order Y₆. Then, an incremental parameter i is set to1 (step 1303) for later use. Then two tests are performed on the y-orderelements, Test 1 (step 1304) and Test 2 (step 1305). In FIG. 13, Tests 1and 2 are shown as being performed in parallel, however they may beperformed serially in any order. The purpose of these multiple tests isto determine different geometrical costs for different geometricalrelationships of the n elements and to test these costs againstdifferent thresholds to facilitate the determination of whether multipleobjects are present, where the determination of the geometrical costs bythe system involve different speed and accuracy levels. Test 1 (1304) isdescribed in more detail later with reference to the flow diagram FIG.14, and Test 2 (1305) is described in more detail later with referenceto the flow diagram FIG. 15.

Tests 1 and 2 are performed iteratively for each consecutive y-orderelement (beginning with the first element, e.g., Y₁, as designated bystep 1303). The geometrical cost determinations of Tests 1 and 2 areconsidered together (step 1306) in order to allow a decision as towhether a ‘cut’ line should be created at the lowest (in they-direction) edge of the current y-order element, i.e., between thatelement and the elements below, thereby defining a boundary betweenvertically displaced objects (step 1307). This cut line creation mayinclude defining a bounding box about the elements considered topossibly belong to the same object, thereby grouping elements for whichthe different geometrical costs were determined to be below thecorresponding confidence thresholds in the sequential y-order iteration.Once this decision is made, the parameter i is incremented to i+1 (step1308) and processing returns to implement Tests 1 and 2 for the nextconsecutive element until the final element of the input is tested.

Test 1 involves determining whether a (first) geometrical cost is morethan a (first) pre-determined threshold. As shown in FIG. 14, this isdone by first determining whether a next consecutive y-order element(i.e., Y_(i+1)) from the y-order element being tested (i.e., Y_(i)) ispresent (step 1401). If not (i.e., the last element is being tested),the (pre)processing ends (step 1402), and the recognition stage 118progresses to the next step of recognition of the actual content of theelements. If a further y-order element is present, the (first) verticaldistance e_(i) between the barycenters of the current y-order element(Y_(i)) and the next consecutive y-order element (Y_(i+1)) is determined(step 1403). This distance represents the first geometrical cost and canbe calculated or measured by pixel count, such that thepre-determination of the first threshold may be done in consideration ofthe pixel resolution of input surface 104. For example, in FIG. 10B thevertical distance e₂ between the barycenters of element 1002 and element1003 is being considered, and in FIG. 11A the vertical distance e₃between the barycenters of element 1003 and element 1004 is considered.

The current first geometrical cost e_(i) is then compared to a (first)pre-determined (barycenter) threshold distance as a first test ofconfidence for there being multiple objects (step 1404). The result ofthis step is a ‘yes’ or ‘no’ determination. The setting of the firstthreshold may be done so a high level of confidence is achieved if alarge barycenter separation of consecutive elements is present. Forexample, in FIG. 10B elements 1002 and 1003 overlap in the y-directionand the distance e₂ between these elements is relatively small. Thereshould be little to no confidence that these elements belong to separatevertically displaced objects (it is noted that the distance e_(i) istaken as an absolute value, since as in FIG. 10B the distance e₂ wouldotherwise be a negative value). Whereas in FIG. 11A, elements 1003 and1004 do not overlap in the y-direction by some margin, and thebarycenter distance e₃ between these elements is relatively large. Thereshould be at least a reasonable amount of confidence that these elementsmay belong to separate vertically displaced objects. The determinationof step 1404, e.g., ‘yes’ or ‘no’, and the first geometrical cost valuee_(i) is output by Test 1 (step 1405) for processing by the multipletest process at step 1306.

Test 2 involves determining whether a (second) geometrical cost is morethan a (second) pre-determined threshold. As shown in FIG. 15, this isdone by first determining whether a next consecutive y-order element(i.e., Y_(i+1)) from the y-order element being tested (i.e., Y_(i)) ispresent (step 1501). If not (i.e., the last element is being tested),the (pre)processing ends (step 1502), and the recognition stage 118progresses to the next step in the recognition of the actual content ofthe elements. This is a similar to step 1401 of Test 1, and this stepmay be combined as a pre-requisite step for the performance of Tests 1and 2 on a given element. If a further y-order element is present, the(second) vertical distance f_(i) between the current y-order element(Y_(i)) and a bounding box defined about the next consecutive andsubsequent y-order elements (Y_(i+1) to Y_(n)) is determined (step1503). This (geometrical boundary) distance represents the secondgeometrical cost and can be calculated or measured by pixel count, suchthat the pre-determination of the second threshold may be done inconsideration of the pixel resolution of the input surface 104.

For example, in FIG. 10C the vertical distance f₂ between the lowestedge (i.e., in the y-direction) of element 1002 and the highest edge ofbounding box 1007 bounding elements 1003-1006 is being considered. InFIG. 11B, the vertical distance f₃ between the lowest edge of element1003 and the highest edge of bounding box 1107 bounding elements1004-1006 is being considered. It is noted that the alternativey-defined edges of the elements and bounding box could be used for thedistance calculation. Further, a bounding box need not be created.Rather, a ‘cut’ line may be created at a y-defined edge of the y-orderelement under consideration (Y) and the distance to a y-defined edge ofthe next consecutive y-order element calculated to determine the secondgeometrical cost.

The current second geometrical cost f_(i) is then compared to a (second)pre-determined (gap) threshold distance as a second test of confidencefor multiple objects (step 1504). The result of this step is a ‘yes’ or‘no’ determination. The setting of the second threshold may be done so ahigh level of confidence is achieved if a large gap between consecutiveelements is present. For example, in FIG. 10C elements 1002 and 1003overlap in the y-direction, and the distance f₂ between these elementsis relatively small. There should be little to no confidence that theseelements belong to separate vertically displaced objects. Whereas inFIG. 11B, elements 1003 and 1004 do not overlap in the y-direction bysome margin, and the distance f₃ between these elements is relativelylarge. Here, there should be at least a reasonable amount of confidencethese elements may belong to separate vertically displaced objects. Thedetermination of step 1504, e.g., ‘yes’ or ‘no’, and the secondgeometrical cost value f; is output by Test 2 (step 1505) for processingby the multiple test process at step 1306.

Returning to FIG. 13, in step 1306 the outputs of the determinations ofTest 1 and Test 2 are combined in order to allow a decision to be madeas to whether multiple objects are present, such as multiline equations.For the example of FIGS. 10B and 10C in which confidence of whether a‘cut’ line should be created beneath element 1002 is tested, the resultof Test 1 may be that the first geometrical cost is not greater than thefirst threshold—e.g., step 1404 returned a ‘no’—and the result of Test 2may be that the second geometrical cost is not greater than the secondthreshold—e.g., step 1504 returned a ‘no’. Since both tests returned a‘no’, the ‘cut’ decision in step 1307 would be to not create a ‘cut’beneath the element 1002, leaving no cuts as depicted in FIG. 10A.

On the other hand, for the example of FIGS. 11A and 11B in whichconfidence of whether a ‘cut’ line should be created beneath element1003 is tested, the result of Test 1 may be that the first geometricalcost is greater than the first threshold—e.g., step 1404 returned a‘yes’—and the result of Test 2 may be that the second geometrical costis greater than the second threshold—e.g., step 1504 returned a ‘yes’.Since both tests returned a ‘yes’, the ‘cut’ decision in step 1307 wouldbe to create a ‘cut’ beneath element 1003. Because earlier tests ofelements 1001 and 1002 result in no ‘cut’ being created, bounding box1108 is positioned about elements 1001-1003 as depicted in FIG. 11C atstep 1307 since the system is confident that object 1108 is a separateobject from any object containing the later y-order elements. Forexample input 1000, continued processing would determine that since eachof elements 1004-1006 overlap in the y-direction with one another, thetests on these elements would also not result in a cut being created.During the subsequent recognition processing, elements 1004-1006 wouldbe considered to belong to a second object.

Depending on the input, the examples of FIGS. 10-15 may return resultsfor certain elements where Test 1 outputs a ‘no’ but Test 2 outputs a‘yes’, and vice-versa. For example, the barycenter distance (firstgeometrical cost) may be relatively large but the gap (secondgeometrical cost) between the elements may be relatively small, whichmay occur with a summation operation as in FIG. 8. In such a situation,the present system may simply consider that there is no confidence inthere being multiple objects defined at the boundary of those elements.Indeed, this may indicate that one measurement is relatively inaccurate,and the other measurement is relatively accurate. Alternatively, otherfactors may be taken into account in order to adjust or hone thethresholds or allow exceptions. This may also be the case when bothtests result in a ‘no’ output.

For example, if a large number of elements are present—i.e., step 1301determines n is a relatively large number—but few or no cuts are createdafter performing the tests on all (or a statistically relevant number)of the elements. The present system may consider more cuts should havebeen created due to the large number of elements that may indicate thepresence of multiple objects, particularly if the y-direction extent ofthe elements and relative sizes of the elements are also taken intoaccount. The present system may then adjust one or both the barycenterand gap thresholds to allow more positive results to occur. This processshould be performed with caution as the return of too many falsepositives will lead to inaccurate recognition in the next stage. Suchdecisions of adjustment can be assisted through the training of thepresent system using a statistically large number of input samples in aninitialization exercise for setting the thresholds. This training canalso be or on an ongoing basis, particularly if the HWR system 114 ishosted on a remote server.

As described earlier in relation to steps 1405 and 1505, themeasured/calculated first and second geometrical costs may also beoutput by the separate tests. As illustrated in FIG. 13, these actualdistances/costs may be considered in step 1307 when making the ‘cut’decision. In one example, the actual value of the geometrical cost of atest that output a ‘no’ determination is compared to the threshold ofthat test to see if the difference is within a certaintolerance/percentage such that the result ‘no’ is changed to a ‘yes’ ifthe cost is within the tolerance. In another example, the actual valueof the geometrical cost of a test that output a ‘no’ determination iscompared to the actual, average or mean size of the elements to see ifthe cost is relatively large compared to the element size(s), such thatthe result ‘no’ is changed to a ‘yes’ if the cost is larger than theelement size(s) by a certain percentage.

As discussed earlier, a further consideration is determining how theresults of the separate tests affect the balance between speed andaccuracy. In the present example, the first test (Test 1) considers thebarycenter distances between consecutive y-order elements. Thedetermination of stroke barycenters, or alternatively or additionallyother stroke factors, and measurement/calculation of distancestherebetween is performed relatively fast, e.g., within units ofmicroseconds. However taking just these distances into account to decidewhere to ‘cut’ may result in many false positives, since stokes factors,such as barycenter displacement, alone are not accurate indicators ofmultiple objects, e.g., the strokes within a single equation may havemany varied sizes such that barycenters of adjacent strokes aredistributed widely but the gaps between the strokes are relativelysmall, such as in FIG. 16. Thus, Test 1 may be considered to providerelatively high processing speed but relatively low recognitionaccuracy.

On other hand, the second test (Test 2) considers the gap orinter-element distances between consecutive y-order elements, and itsuse of distances between bounding boxes or other grouping mechanisms ofstrokes provides a reasonably accurate indicator of multiple objects.However, the establishment of those groups may be performed relativelyslowly, e.g., within tens to hundreds of microseconds. Thus, Test 2 maybe considered to provide relatively high recognition accuracy butrelatively low processing speed. As such, the combination of the twotests allows a balance between speed and accuracy, and this balance canbe adjusted (e.g., by adjusting or weighting the correspondingthresholds) based on the needs of the system, e.g., speed is favoredover accuracy, or vice-versa.

More precisely, the test which determines and compares displacement ofcommon geometrical features of the content of the elements, e.g., thebarycenter of the strokes may result in a relatively high number of cutsbut an unacceptable proportion of these may be false positives, leadingto higher inaccuracy. Whereas the test that determines and comparesdisplacement of common or non-common geometrical features of theelements themselves, e.g., the same or different edges of the boundingboxes of the elements provides a relatively lower number of falsepositives but not enough cuts, leading to higher processing time.

Further improvement of the accuracy can be provided by an alternativeexample of the second geometrical test 1305, illustrated in FIGS.12A-12C. Like the second test example of FIG. 11, this alternativesecond test (Test 2) involves determining whether a second geometricalcost is more than the second pre-determined threshold, where the secondgeometrical cost is determined from a (second) distance between y-orderelements. However, unlike the previous example of Test 2, the second(gap) distance is determined from considering nearest neighbors in they-order rather than just between consecutive y-order elements. Thisalternative test is now described with reference to the example flowdiagram FIG. 17.

First a non-incremental parameter j is set to i (step 1701) for use inlater steps, and the incremental parameter i is set to i+1 (step 1702)to allow iteration. After these initializations, it is determinedwhether a next consecutive y-order element (i.e., Y_(i) due to theincrement of the parameter i) from the y-order element being tested(i.e., Y_(j) due to the setting of the parameter j) is present (step1703). So long as further elements are found, a geometrical area as asearch zone is determined for the next consecutive y-order element Y_(i)(step 1704). The extent of this search zone is adjustable and used todetermine the minimum distance between the next element(s) (in they-order) and the current element under consideration (i.e., Y_(j)) andany prior elements in the y-order (i.e., Y₁-Y_(j−1)) to determine thesecond geometrical cost.

FIG. 12A shows search zone 1201 established above (i.e., in they-direction) element 1004, being the next consecutive y-order elementfrom current element 1003 (as depicted in FIG. 11). FIG. 12B showssearch zone 1202 established above element 1005, being the nextconsecutive y-order element from element 1004. The search zone isestablished in an area that has a width (i.e., in the x-direction) thatis three times the width x of the element of the search where this areais centered on that element, e.g., in FIG. 12A the area has a width 3x₄where x₄ is the width of the element 1004 and in FIG. 12B the area has awidth 3x₅ where x₅ is the width of the element 1005. This geometricalarea in which to search for earlier y-order elements for determinationof the closest point of separation between the elements at a potential‘cut’ position, is used to provide ‘padding’ about elements so thatconsideration of distances between a sufficient and meaningful number ofseparated elements is provided. The amount of padding is adjustable,such that another integer or fractional width of the elements can beused and based on some other factor unrelated to the element width. Forexample, the padding could be provided by applying a characteristic ofthe handwritten strokes, such as the scale estimation value used by therecognizer in the recognition processing of the handwritten characters,symbols, etc. Accordingly, in FIG. 12 the search zone could be providedby establishing the area to be centered on each of elements 1004-1006with a padding amount of three times (or other factor) the scaleestimation value on each (horizontal) side of the elements. Those ofordinary skill in the art understand stroke characteristics, such asscale estimation values, to provide statistical character probabilityanalysis.

Upon establishment of the search zone, it is determined if there are anyelements from the current element being tested and prior elements (i.e.,Y₁-Y_(j)) within the search zone (step 1705). If none of the y-orderelements Y₁-Y_(j) are within the search zone, the processing returns tostep 1702 to iterate to a next element to be searched. If at least oneof the y-order elements Y₁-Y_(j) is within the search zone, the verticaldistance(s) f_(im) (where m=the number of the elements Y₁-Y_(j) in thesearch zone) between the current next element any each of the elementsY₁-Y_(j) above that element is calculated/measured and the minimum ofthese distances is determined (step 1706). For example, in FIG. 12A onlyelement 1002 is in the search zone 1201 (where element 1003 is currentlybeing tested) such that the distance f₄₁ between the element 1004 andelement 1002 is returned as the minimum (gap) distance of element 1004.While the search zone is discussed as being established for elementsbelow the element being tested to determine positional relationshipswith those elements above the bottom (i.e., in the y-direction) of theelement being tested, those of ordinary skill in the art understand thatthe search zone may equally be established for elements above theelement being tested to determine positional relationships with thoseelements below the bottom of the element being tested, for example.

In order to determine whether this minimum distance should be consideredin later processing as the second geometrical cost (described later), itis first determined if a minimum distance f has been previously stored,for example, in the memory 108 (step 1707). If so, the determinedminimum distance is compared with this previously stored minimumdistance f (step 1708), and if not, the determined minimum distance isstored as the minimum distance f (step 1709). For example, in theprocessing of element 1004 in FIG. 12A, there is no previously storedminimum distance, so the minimum distance of element 1004 is stored.There may be input scenarios in which no minimum distance is determinedsince there are no y-order elements present in the search zone(s) of anytested element or there are no elements below the element being tested(i.e., the last element). This is accounted for in later steps of thisexample, however other ways to deal with this scenario include providingadjustment of the search zone in order to ensure that at least oneminimum distance is calculated, or an arbitrarily second geometricalcost may be set in the initialization stage, e.g., a (pseudo) randomlygenerated cost value approaching infinity.

In the comparison of step 1708, if the current minimum distance isgreater than the stored minimum distance, it is discarded and processingreturns to step 1702, since this means that there is another elementpresent which is closer to the potential first object than the elementpresently under consideration. On the other hand, if the currentdetermined minimum distance is less than the stored minimum distanceprocessing moves to step 1709 so that the current determined minimumdistance is stored in place of the currently stored minimum distance f,and then processing returns to step 1702. For example, from FIGS. 12Aand 12B it can be seen that element 1005 is closer to the element 1003within its search zone 1202 than element 1004 is to element 1002 withinits search zone 1201. Therefore, the minimum distance of element 1005(being distance f₅₁ which is less than distance f₅₂) is stored in placedof the previously stored minimum distance f₄₂ of the element 1004 whichis larger.

Once all elements under the current test element (e.g., element 1003 inFIG. 12) have been considered, step 1703 returns a ‘no’ and processingmoves to the final stage of the alternative second test. In this stage,the incremental parameter i is first reset (step 1710) for use in thesecond test for the following consecutive elements (this step can followthe other steps of this stage). It is again determined whether a minimumdistance f has been stored in the memory 108 (step 1711), and if not,the determination of ‘no’ with respect to the second geometrical costbeing more than the second threshold is output to step 1306 (step 1712).This step is similar to step 1707 and repeated in this step to accountfor the above-described scenario in which no minimum distance isdetermined and stored in this alternative Test 2. If there is a storedminimum distance, being the second geometrical cost, this value iscompared to the (second) gap threshold distance, as the second test ofconfidence (step 1713). Like the earlier example of Test 2, the settingof the second threshold in this alternative method may be done so a highlevel of confidence is achieved if a large gap between the testedelements is present. The result of this step is a ‘yes’ or ‘no’determination, and the second geometrical cost value f is output by Test2 (step 1714) for processing at step 1306.

It was earlier described in relation to FIGS. 11A and 11B that theresult of Test 1 may be that the first geometrical cost is greater thanthe first threshold, and the result of Test 2 may be that the secondgeometrical cost is greater than the second threshold, such that the‘cut’ decision in step 1307 would be to create a ‘cut’ beneath element1003. However, the second threshold may be set for Test 2 such that inthis example it falls between the second geometrical cost determined inthe example method of FIG. 14 (i.e., the gap distance f₃ of FIG. 11B)and the second geometrical cost determined in the alternative method ofFIG. 17 (i.e., the minimum distance f₅₁ of FIG. 12B), since the gapdistance f₃ is less than the minimum distance f₅₁.

In this situation, the simpler Test 2 of the first example in which thebounding box of all elements below the element being tested is used tocreate the second geometrical cost will yield a ‘no’ determination. Inthis case, a ‘cut’ would not subsequently be created beneath element1003. This would lead to bounding box 1109 being defined around all ofelements 1001-1006 as illustrated in FIG. 11D, since continuedprocessing would determine that elements 1004-1006 belong to the sameobject. On the other hand, the more complex Test 2 of the second examplein which each element below the element being tested is individuallyused to create the second geometrical cost will yield a ‘yes’determination. In which case, a ‘cut’ would subsequently be createdbeneath element 1003. This leads to bounding box 1108 being definedabout elements 1001-1003 as depicted in FIG. 11C.

The alternative test may result in a more accurate determination ofthere being separate 2D objects in example input 1000. As such, thealternative tests for the second geometrical cost may both be performedto provide adjustment of the results returned from Test 2 and/oradjustment of the first and second geometrical cost thresholds.

As with the earlier example described with respect to FIGS. 6 and 7, thetemporal or time-order entry of the strokes/elements may also be takeninto account to adjust the first and second geometrical costs of theexamples described in relations to FIGS. 10-17.

The above described examples may include recognition performed duringincremental recognition of multiple object elements, such as the strokesin equations, in which the HWR system 114 includes a device, such as anincrementer, which continuously parses the input strokes/elements to therecognition engine (after preprocessing if present) upon input (or shortdelay thereafter; typically measured by strokes) so that recognition ofthe strokes is performed and the recognized elements are stored (cached)in the memory 108. In this way, the multiple object testing can beperformed in parallel to the recognition so as soon as a separate objectis determined, the recognition processing of the strokes within thatobject has already been performed such that these strokes need not beprocessed again (i.e., re-recognized) when processing the next andsubsequent objects, thereby further optimizing speed of the recognitionprocess.

The above-described example application of the methods and systemsdescribed herein are is to a handwritten input of vertically displacedobjects, such as mathematical equations. As described earlier, anyhandwritten input of a 2D system of objects, such as drawings, diagrams,music, chemical formulas, etc., in which multiple objects are input andneed to be separately recognized is also applicable as the describedmethods and systems provide recognition of multiple text, symbols andobjects at any orientation. Further, as described earlier, not onlyvertical lists, for example, can be recognized, but the describedmethods and system also provide recognition of horizontal lists andarbitrarily placed objects.

Further, as mentioned earlier, the various examples described herein canbe applied to forms of input for recognition other than handwriting,such as offline recognition in which images rather than digital ink arerecognized, for example, the elements may be input as an image capturedas a photograph of writing on paper or a whiteboard, digitally capturedon an interactive smartboard, etc.

The described methods and systems increase processing and recognitionspeed of multiple objects, such as a vertical list of multiplemathematical equations, as multiple object recognition is performedindependent of the recognition of the objects themselves. Further,complex multiple object input, such as complex systems of abstractarithmetical equations, is enabled without confused recognition results.Furthermore, writing of multiple objects, such as equations, does notrequire specific user action for recognition, such as creating a newwriting area, tapping a new line button, etc. Further still, matching ofstrokes/elements to artificial structure, such as tables, is notrequired for recognition of multiple objects. Further, no learning ortraining of the algorithm required, however this could be performed toimprove results.

While the foregoing has described what is considered to be the best modeand/or other examples, it is understood that various modifications maybe made therein and that the subject matter disclosed herein may beimplemented in various forms and examples, and that they may be appliedin numerous other applications, combinations, and environments, onlysome of which have been described herein. Those of ordinary skill inthat art will recognize that the disclosed aspects may be altered oramended without departing from the true spirit and scope of the subjectmatter. Therefore, the subject matter is not limited to the specificdetails, exhibits, and illustrated examples in this description. It isintended to protect any and all modifications and variations that fallwithin the true scope of the advantageous concepts disclosed herein.

I claim:
 1. A method of recognizing handwritten input of multipleobjects to a computing device, the computing device comprising aprocessor and at least one application for recognizing the input undercontrol of the processor, the method comprising the steps of:determining, with the application, at least one geometrical feature of aplurality of elements of the input; comparing, with the application, thedetermined at least one geometrical feature with at least onepre-determined geometrical threshold to determine a positive or negativeresult; and deciding a number of objects to which the elements belong asbeing one or a plurality based on the comparing step, wherein thedeciding step associates a determination of the negative result with theelements belonging to one object, and the deciding step associates adetermination of a positive result with the elements belonging tomultiple objects, wherein the at least one geometrical feature includesone or more distances between pairs of elements of the plurality ofelements, wherein the one or more distances is between one or morefactors of the content of each element of each pair of elements, whereinthe one or more factors includes at least one of a factor common to theelements of each pair of elements and a geometrical boundary includingeach element, wherein the comparison includes comparing a first distancewith a first pre-determined distance threshold and a second distancewith a second pre-determined distance threshold for each pair ofelements, and wherein, for each pair of elements: the first distance isthe distance between the common factor of the elements; the seconddistance is the distance between the geometrical boundary of theelements; the first pre-determined distance threshold is a common factordistance threshold; and the first pre-determined distance threshold is ageometrical boundary threshold.
 2. A method as claimed in claim 1,wherein: each element of each pair of elements represents one or morehandwritten strokes; the common factor is the barycenter of the one ormore strokes; the at least one pre-determined geometrical threshold is abarycenter distance threshold; and the comparison yields a positiveresult if the barycenter distance determined for a pair of elements isgreater than the barycenter distance threshold, such that the elementsof the pair of elements are considered as belonging to differentobjects.
 3. A method as claimed in claim 1, wherein: the at least onepre-determined geometrical threshold is a geometrical boundary distancethreshold; and the comparison yields a positive result if thegeometrical boundary distance determined for a pair of elements isgreater than the geometrical boundary distance threshold, such that theelements of the pair of elements are considered as belonging todifferent objects.
 4. A method as claimed in claim 1, wherein thecomparison yields a positive result for a pair of elements if both thefirst and second distances are greater than the respective first andsecond pre-determined distance thresholds, such that the elements of thepair of elements are considered as belonging to different objects.
 5. Amethod as claimed in claim 1, wherein: each element of each pair ofelements represents one or more handwritten strokes; and the commonfactor is the barycenter of the one or more strokes.
 6. A method asclaimed in claim 1, wherein the elements of each pair of elements aregeometrically adjacent.
 7. A method as claimed in claim 1, furthercomprising determining, with the application, at least one of apositional and temporal order of input of the elements of the pluralityof elements.
 8. A method as claimed in claim 7, wherein the at least onegeometrical threshold is pre-determined with consideration of thedetermined temporal order of input of the elements.
 9. A method asclaimed in claim 7, wherein, for at least one pair of the pairs ofelements: the determining of the at least one geometrical featureincludes: determining, with the application, the geometrical boundarydistances between pairs of elements which each contain a first elementhaving a first positional order relationship with one element of the atleast one pair and a second element having a second positional orderrelationship with the other element of the at least one pair; anddetermining, with the application, the minimum distance of thedetermined geometrical boundary distances; the at least onepre-determined geometrical threshold includes a geometrical boundarydistance threshold; the comparison includes comparing the determinedminimum geometrical boundary distance with the geometrical boundarydistance threshold; and the comparison yields a positive result if thedetermined minimum geometrical boundary distance is greater than thegeometrical boundary distance threshold, such that the elements of theat least one pair are considered as belonging to different objects. 10.A method as claimed in claim 9, wherein the positional order isdirectional, the first and second directional relationships being firstand second directions from the elements of the at least one pair,respectively.
 11. A method as claimed in claim 9, wherein the pairs offirst and second elements contain first elements within a geometricalarea of the second element.
 12. A method as claimed in claim 11,wherein: each element of each pair of elements represents one or morehandwritten strokes; and the geometrical area is based on acharacteristic of the one or more handwritten strokes.
 13. A computerprogram product, comprising a non-transitory computer usable mediumhaving a computer readable program code embodied therein, said computerreadable program code adapted to be executed to implement a method forrecognizing handwritten input of multiple objects to a computing device,the computing device comprising a processor and at least one applicationfor recognizing the input under control of the processor, the methodcomprising the steps of: determining, with the application, at least onegeometrical feature of a plurality of elements of the input; comparing,with the application, the determined at least one geometrical featurewith at least one pre-determined geometrical threshold to determine apositive or negative result; deciding a number of objects to which theelements belong as being one or a plurality based on the comparing step,wherein the deciding step associates a determination of the negativeresult with the elements belonging to one object, and the deciding stepassociates a determination of a positive result with the elementsbelonging to multiple objects, the computer program product furthercomprising determining, with the application, at least one of apositional and temporal order of input of the elements of the pluralityof elements, wherein the at least one geometrical feature includes oneor more distances between pairs of elements of the plurality ofelements, wherein, for at least one pair of the pairs of elements: thedetermining of the at least one geometrical feature includes:determining, with the application, the geometrical boundary distancesbetween pairs of elements which each contain a first element having afirst positional order relationship with one element of the at least onepair and a second element having a second positional order relationshipwith the other element of the at least one pair; and determining, withthe application, the minimum distance of the determined geometricalboundary distances; the at least one pre-determined geometricalthreshold includes a geometrical boundary distance threshold; thecomparison includes comparing the determined minimum geometricalboundary distance with the geometrical boundary distance threshold; andthe comparison yields a positive result if the determined minimumgeometrical boundary distance is greater than the geometrical boundarydistance threshold, such that the elements of the at least one pair areconsidered as belonging to different objects.